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SET C
PART A β Chemistry
1. Which of the following salts is the most basic in aqueous solution?
(A) πΆπ»3πΆπππΎ (B) πΉππΆπ3
(C) ππ(πΆπ»3πΆππ)2 (D) π΄π(πΆπ)3
2. Which of the following compounds will be suitable for Kjeldahlβs method for nitrogen estimation?
(A)
(B)
(C)
(D)
3. Which of the following are Lewis acids?
(A) π΄ππΆπ3 and πππΆπ4
(B) ππ»3 and π΅πΆπ3
(C) π΅πΆπ3 and π΄ππΆπ3
(D) ππ»3 and πππΆπ4
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4. Phenol on treatment with πΆπ2 in the presence of NaOH followed by acidification produces compound X as
the major product. X on treatment with (πΆπ»3πΆπ)2 in the presence of catalytic amount of π»2ππ4 produces:
(A)
(B)
(C)
(D)
5. An alkali is titrated against an acid with methyl orange as indiactor, which of the following is a correct
combination?
(A) Base Acid End point
Strong strong Pinkish red to yellow
(B) Base Acid End pointWeak strong yellow to Pinkish red
(C) Base Acid End point
Strong Strong Pink to colourless
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(D) Base Acid End pointWeak Srtong Colourless to pink
6. An aqueous solution contains 0.10 π π»2π and 0.20 M π»πΆπ. If the equilibrium constants for the formation of
π»πβ from H2S is 1.0 Γ 10β7 and that of S2β from π»πβ ions is 1.2 Γ 10β13 then the concentration of π2β ions
in aqueous solution is:
(A) 3 Γ 10β20
(B) 6 Γ 10β21
(C) 5 Γ 10β19
(D) 5 Γ 10β8
7. The combustion of benzene (π) gives πΆπ2(π) and π»2π(π). Given that heat of combustion of benzene at
constant volume is β3263.9 ππ½ πππβ1 at 25ππΆ; heat of combustion (ππ ππ½ πππβ1) of benzene at constant
pressure will be:
(π = 8.314 π½πΎβ1 πππβ1)
(A) β452.46 (B) 3260 (C) β3267.6 (D) 4152.6
8. The compound that does not produce nitrogen gas by thermal decomposition is:
(A) (ππ»4)2πΆπ2π7 (B) ππ»4ππ2
(C) (ππ»4)2ππ4 (D) π΅π(π3)2
9. How long (approximate) should water be electrolyzed by passing through 100 amperes current so that the
oxygen released can completely burn 27.66 g of diborane? (Atomic weight of B = 10.8 u)
(A) 0.8 hours
(B) 3.2 hours
(C) 1.6 hours
(D) 6.4 hours
10. Total number of lone pair of electrons in I3β ions is:
(A) 6 (B) 9 (C) 12 (D) 3
11. When metal βMβ is treated with NaOH, a white gelatinous precipitate βXβ is obtained, which is soluble in
excess of NaOH. Compound βXβ when heated strongly gives an oxide which is used in chromatography as an
adsorbent. The metal βMβ is:
(A) Ca (B) Al (C) Fe (D) Zn
12. According to molecular orbital theory, which of the following will not be a viable molecule?
(A) π»π2+ (B) π»2
β (C) π»22β (D) π»π2
2+
13. The increasing order of basicity of the following compounds is:
(i)
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(ii)
(iii)
(iv)
(A) (ii) < (i) < (iii) <(iv)
(B) (ii) < (i) < (iv) < (iii)
(C) (iv) < (ii) < (i) < (iii)
(D) (i) < (ii) < (iii) < (iv)
14. Which type of βdefectβ has the presence of cations in the interstitial sites?
(A) Vacancy defect
(B) Frenkel defect
(C) Metal deficiency defect
(D) Schottky defect
15. Which of the following compounds contain(s) no covalent bond(s)?
πΎπΆπ, ππ»3, π2, π΅2π»6, π»2ππ4
(A) πΎπΆπ, π»2ππ4
(B) πΎπΆπ
(C) πΎπΆπ, π΅2π»6
(D) πΎπΆπ, π΅2π»6, ππ»3
16. The oxidation states of πΆπ in [πΆπ(π»2π)6]πΆπ3, [πΆπ(πΆ6π»6)2], and πΎ2[πΆπ(πΆπ)2(π)2(π)2(ππ»3)] respectively
are:
(A) +3,+2 and +4
(B) +3, 0 and +6
(C) +3, 0 and +4
(D) +3,+4 and +6
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17. Hydrogen peroxide oxidises [πΉπ(πΆπ)6]4βto [Fe(πΆπ)6]
3β in acidic medium but reduces
[πΉπ(πΆπ)6]3βto[πΉπ(πΆπ)6]
4β in alkaline medium. The other products formed are, respectively:
(A) (π»2π + π2) and (π»2π + ππ»β)
(B) π»2π and (π»2π + π2)
(C) π»2π and (π»2π + ππ»β)
(D) (π»2π + π2) and H2π
18. Glucose on prolonged heating with π»πΌ gives:
(A) 1 β Hexene
(B) Hexanoic acid
(C) 6 β iodohexanal
(D) n β Hexane
19. The predominant form of histamine present in human blood is (ππΎπ , Histidine = 60. )
(A)
(B)
(C)
(D)
20. The recommended concentration of fluoride ion in drinking water is up to 1 ppm as fluoride ion is required
to make teeth enamel harder by converting [3πΆπ3(ππ4)2 . πΆπ(ππ»)2] to:
(A) [3(πΆππΉ2). πΆπ(ππ»)2]
(B) [3πΆπ3(ππ4)2. πΆππΉ2]
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(C) [3{πΆπ(ππ»)2}. πΆππΉ2]
(D) [πΆππΉ2]
21. Consider the following reaction and statement:
[πΆπ(ππ»3)4π΅π2]+ + π΅πβ β [πΆπ(ππ»3)3π΅π3] + ππ»3
(i) Two isomers are produced if the reactant complex ion is a cis β isomer.
(ii) Two isomers are produced if the reactant complex ion is a trans β isomer.
(iii) Only one isomer is produced if the reactant complex ion is a trans β isomer.
(iv) Only one is produced if the reactant complex ion is a cis β isomer.
The correct statements are:
(A) (i) and (iii)
(B) (iii) and (iv)
(C) (ii) and (iv)
(D) (i) and (ii)
22. The trans-alkenes are formed by the reduction of alkynes with:
(A) πππ΅π»4 (B) ππ πππβ . ππ»3
(C) ππ β π»πΆπ (D) π»2 β ππ πΆ, π΅πππ4β
23. The ratio of mass percent of C and H of an organic compound (πΆππ»πππ) is 6 : 1. If one molecule of the
above compound (πΆππ»πππ) contains half as much oxygen as required to burn one molecule of compound
πΆππ»π completely to πΆπ2 and π»2π. The empirical formula of compound πΆππ»πππ is:
(A) πΆ2π»4π (B) πΆ3π»4π2 (C) πΆ2π»4π3 (D) πΆ3π»6π3
24. Phenol reacts with methyl chloroformate in the presence of ππππ» to form product A. A reacts with π΅π2 to
form product B. A and Bare respectively:
(A)
(B)
(C)
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(D)
25. The major product of the following reaction is:
(A)
(B)
(C)
(D)
26. Which of the following lines correctly show the temperature dependence of equilibrium constant, K, for an
exothermic reaction?
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(A) B and C
(B) C and D
(C) A and D
(D) A and B
27. The major product formed in the following reaction is:
(A)
(B)
(C)
(D)
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28. An aqueous solution contains an unknown concentration of π΅π2+. When 50 mL of a 1 M solution of
ππ2ππ4 is added, π΅πππ4 just begins to precipitate. The final volume is 500 mL. The solubility product of
π΅πππ4 is 1 Γ 10β10. What is the original concentration of π΅π2+?
(A) 2 Γ 10β9π
(B) 1.1 Γ 10β9π
(C) 1.0 Γ 10β10π
(D) 5 Γ 10β9π
29. At 518ππΆ, the rate of decomposition of a sample of gaseous acetaldehyde, initially at a pressure of 363
Torr, was 1.00 ππππ π β1 when 5% had reacted and 0.50 ππππ π β1 when 33% had reacted. The order of the
reaction is:
(A) 3
(B) 1
(C) 0
(D) 2
30. For 1 molal aqueous solution of the following compounds, which one will show the highest freezing point?
(A) [πΆπ(π»2π)5πΆπ]πΆπ2. π»2π
(B) [πΆπ(π»2π)4πΆπ2]πΆπ. 2π»2π
(C) [πΆπ(π»2π)3πΆπ3]. 3π»2π
(D) [πΆπ(π»2π)6]πΆπ3
PART B β Mathematics
31. The integral β«sin2 π₯ cos2 π₯
(sin5 π₯+cos3 π₯ sin2 π₯+sin3 π₯ cos2 π₯+cos5 π₯)2ππ₯ is equal to:
(A) β1
3(1+tan3 π₯)+ πΆ (B)
1
1+cot3 π₯+ πΆ
(C) β1
1+cot3 π₯+ πΆ (D)
1
3(1+tan3 π₯)+ πΆ
32. Tangents are drawn to the hyperbola 4π₯2 β π¦2 = 36 at the points P and Q. If these tangents intersect at the
point π(0, 3) then the area (in sq. units) of Ξπππ is:
(A) 54β3 (B) 60β3 (C) 36β5 (D) 45β5
33. Tangent and normal are drawn at π(16, 16) on the parabola π¦2 = 16π₯, which intersect the axis of the
parabola at A and B, respectively. If C is the centre of the circle through the points P, A and B and β πΆππ΅ = π,
then a value of tan π is:
(A) 2 (B) 3 (C) 4
3 (D)
1
2
34. Let οΏ½βοΏ½ be a vector coplanar with the vectors π = 2πΜ + 3πΜ β οΏ½ΜοΏ½ and οΏ½βοΏ½ = πΜ + οΏ½ΜοΏ½. If οΏ½βοΏ½ is perpendicular to π and
οΏ½βοΏ½ β οΏ½βοΏ½ = 24, then |οΏ½βοΏ½ |2 is equal to:
(A) 315 (B) 256 (C) 84 (D) 336
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35. If πΌ, π½ β πΆ are the distinct roots, of the equation π₯2 β π₯ + 1 = 0, then πΌ101 + π½107 is equal to:
(A) 0 (B) 1 (C) 2 (D) β1
36. Let π(π₯) = cos π₯2, π(π₯) = βπ₯, and πΌ, π½(πΌ < π½) be the roots of the quadratic equation 18π₯2 β 9ππ₯ +
π2 = 0. Then the area (in sq. units) bounded by the curve π¦ = (πππ) (π₯) and the lines π₯ = πΌ, π₯ = π½ and π¦ = 0,
is:
(A) 1
2(β3 + 1) (B)
1
2(β3 β β2)
(C) 1
2(β2 β 1) (D)
1
2(β3 β 1)
37. The sum of the co-efficient of all odd degree terms in the expansion of (π₯ + βπ₯3 β 1)5+
(π₯ β βπ₯3 β 1)5, (π₯ > 1) is:
(A) 0 (B) 1 (C) 2 (D) β1
38. Let π1, π2, π3, β¦β¦ , π49 be in A.P. such that β π4π+1 = 41612π=0 and π9 + π43 = 66. If π1
2 + π22 + β―+
π172 = 140π, then m is equal to:
(A) 68 (B) 34 (C) 33 (D) 66
39. If β (π₯π β 5)9π=1 = 9 and β (π₯π β 5)29
π=1 = 45, then the standard deviation of the 9 items π₯1, π₯2, β¦ . , π₯9 is:
(A) 4 (B) 2 (C) 3 (D) 9
40. PQR is a triangular park with PQ = PR = 200m. A T.V. tower stands at the mid-point of QR. If the angles of
elevation of the top of the tower at P, Q and R are respectively 45π, 30π and 30π, then the height of the tower
(in m) is:
(A) 50 (B) 100β3 (C) 50β2 (D) 100
41. Two sets A and B are as under:
π΄ = {(π, π) β π Γ π βΆ |π β 5| < 1 and |π β 5| < 1};
π΅ = {(π, π) β π Γ π : 4(π β 6)2 + 9(π β 5)2 β€ 36}. Then:
(A) π΄ β π΅
(B) π΄ β© π΅ = π (an empty set)
(C) Neither π΄ β π΅ nor π΅ β π΄
(D) π΅ β π΄
42. From 6 different novels and 3 different dictionaries, 4 novels and 1 dictionary are to be selected and
arranged in a row on a shelf so that the dictionary is always in the middle. The number of such arrangements is:
(A) Less than 500
(B) At least 500 but less than 750
(C) At least 750 but less than 1000
(D) At least 1000
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43. Let π(π₯) = π₯2 +1
π₯2 and π(π₯) = π₯ β1
π₯, π₯ β π β {β1, 0, 1}. If β(π₯) =
π(π₯)
π(π₯), then the local minimum value of
β(π₯)is:
(where C is a constant of integration)
(A) β3 (B) β2β2 (C) 2β2 (D) 3
44. For each π‘ β π , let [π‘] be the greatest integer less than or equal to t. Then limπ₯β0+
π₯ ([1
π₯] + [
2
π₯] + β―+ [
15
π₯])
(A) Is equal to 15
(B) IS equal to 120
(C) Does not exist (in R)
(D) Is equal to 0
45. The values of β«sin2 π₯
1+2π₯
π
2
βπ
2
ππ₯ is:
(A) π
2 (B) 4π (C)
π
4 (D)
π
8
46. A bag contains 4 red and 6 black balls. A ball is drawn at random from the bag, its colour is observed and
this ball along with two additional balls of the same colour are returned to the bag. If now a ball is drawn at
random from the bag, then the probability that this drawn ball is red, is:
(A) 2
5 (B)
1
5 (C)
3
4 (D)
3
10
47. The length of the projection of the line segment joining the points (5, -1, 4) and (4, -1, 3) on the plane, π₯ +
π¦ + π§ = 7 is:
(A) 2
3 (B)
1
3 (C) β
2
3 (D)
2
β3
48. If sum of all the solutions of the equation 8 cosπ₯ . (cos (π
6+ π₯) . cos (
π
6β π₯) β
1
2) = 1 in [0, π] is ππ, then
k is equal to:
(A) 13
9 (B)
8
9 (C)
20
9 (D)
2
3
49. A straight line through a fixed point (2, 3) intersects the coordinate axes at distinct points P and Q. If O is
the origin and the rectangle OPRQ is completed, then the locus of R is:
(A) 2π₯ + 3π¦ = π₯π¦ (B) 3π₯ + 2π¦ = π₯π¦
(C) 3π₯ + 2π¦ = 6π₯π¦ (D) 3π₯ + 2π¦ = 6
50. Let A be the sum of the first 20 terms and B be the sum of the first 40 terms of the series
12 + 2 β 22 + 32 + 2 β 42 + 52 + 2 β 62 + β―.
If π΅ β 2π΄ = 100π, then π is equal to:
(A) 248 (B) 464 (C) 496 (D) 232
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51. If the curves π¦2 β 6π₯, 9π₯2 + ππ¦2 = 16 intersect each other at right angles, then the value of b is:
(A) 7
2 (B) 4 (C)
9
2 (D) 6
52. Let the orthocentre and centroid of a triangle be π΄(β3, 5) and π΅(3, 3) respectively. If C is the circumcentre
of this triangle, then the radius of the circle having line segment AC as diameter, is:
(A) 2β10 (B) 3β5
2 (C)
3β5
2 (D) β10
53. Let π = {π‘ β π : π(π₯) = |π₯ β π| β (π|π₯| β 1) sin|π₯| is not differentiable at π‘}. Then the set S is equal to:
(A) {0} (B) {π}
(C) {0, π} (D) π (an empty set)
54. If |π₯ β 4 2π₯ 2π₯2π₯ π₯ β 4 2π₯2π₯ 2π₯ π₯ β 4
| = (π΄ + π΅π₯) (π₯ β π΄)2, then the ordered pair (A, B) is equal to:
(A) (β4,3) (B) (β4, 5) (C) (4, 5) (D) (β4,β5)
55. The Boolean expression ~(π β¨ π) β¨ (~π β§ π) is equivalent to:
(A) π (B) π (C) ~π (D) ~π
56. If the system of linear equations
π₯ + ππ¦ + 3π§ = 0
3π₯ + ππ¦ β 2π§ = 0
2π₯ + 4π¦ β 3π§ = 0
has a non-zero solution (π₯, π¦, π§), then π₯π§/π¦2 is equal to:
(A) 10 (B) β30 (C) 30 (D) β10
57. Let π = {π₯ β π βΆ π₯ β₯ 0 and 2|βπ₯ β 3| + βπ₯ (βπ₯ β 6) + 6 = 0}. Then S:
(A) Contains exactly one element
(B) Contains exactly two elements
(C) Contains exactly four elements
(D) Is an empty set
58. If the tangent at (1, 7) to the curve π₯2 = π¦ β 6 touches the circle π₯2 + π¦2 + 16π₯ + 12π¦ + π = 0 then the
value of c is:
(A) 185 (B) 85 (C) 95 (D) 195
59. Let π¦ = π¦(π₯) be the solution of the differential equation
sin π₯ππ¦
ππ₯+ π¦ cos = 4π₯, π₯ β (0, π). If π¦ (
π
2) = 0, then π¦ (
π
6) is equal to:
(A) β8
9β3π2 (B) β
8
9π2 (C) β
4
9π2 (D)
4
9β3π2
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60. If πΏ1 is the line of intersection of the planes 2π₯ β 2π¦ + 3π§ β 2 = 0, π₯ β π¦ + π§ + 1 = 0 and πΏ2 is the line of
intersection of the planes π₯ + 2π¦ β π§ β 3 = 0, 3π₯ β π¦ + 2π§ β 1 = 0, then the distance of the origin from the
plane, containing the lines πΏ1 and πΏ2 is:
(A) 1
3β2 (B)
1
2β2 (C)
1
β2 (D)
1
4β2
PART C β Physics
61. The angular width of the central maximum in a single slit diffraction pattern is 60π. The width of the slit is
1ππ. The slit is illuminated by monochromatic plane waves. If another slit of same width is made near it,
Youngβs fringes can be observed on a screen placed at a distance 50 cm from the slits. If the observed fringe
width is 1 cm, what id slit separation distance?
(i.e. distance between the centres of each slit.)
(A) 50 ππ
(B) 75 ππ
(C) 100 ππ
(D) 25 ππ
62. An electron from various excited states of hydrogen atom emit radiation to come to the ground state. Let
ππ, ππ be the de Broglie wavelength of the electron in the ππ‘β state and the ground state respectively. Let β§π be
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the wavelength of the emitted photon in the transition from the ππ‘β state to the ground state. For large n, (A, B
are constants)
(A) β§πβ π΄ + π΅ππ (B) β§π2β π΄ + π΅ππ
2
(C) β§π2β π (D) β§πβ π΄ +
π΅
ππ2
63. The reading of the ammeter for a silicon diode in the given circuit is:
(A) 15 ππ΄ (B) 11.5 ππ΄ (C) 13.5 ππ΄ (D) 0
64. The density of a material in the shape of a cube is determined by measuring three sides of the cube and its
mass. If the relative errors in measuring the mass and length are respectively 1.5% and 1%, the maximum error
in determining the density is:
(A) 3.5%
(B) 4.5%
(C) 6%
(D) 2.5%
65. An electron, a proton and an alpha particle having the same kinetic energy are moving in circular orbits of
radii ππ , ππ, ππΌ respectively in a uniform magnetic field B. The relation between ππ , ππ, ππΌ is:
(A) ππ < ππ = ππΌ (B) ππ < ππ < ππΌ
(C) ππ < ππΌ < ππ (D) ππ > ππ = ππΌ
66. Three concentric metal shells A, B and C of respective radii a, b and c (a < b <c) have surface charge
densities +π,βπ and +π respectively. The potential of shell B is:
(A) π
π0[π2βπ2
π+ π]
(B) π
π0[π2βπ2
π+ π]
(C) π
π0[π2βπ2
π+ π]
(D) π
π0[π2βπ2
π+ π]
67. Two masses π1 = 5 ππ and π2 = 10 ππ , connected by an inextensible string over a frictionless pulley,
are moving as shown in the figure. The coefficient of friction of horizontal surface is 0.15. The minimum
weight m that should be put on top of π2 to stop the motion is:
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(A) 27.3 ππ
(B) 43.3 ππ
(C) 10.3 ππ
(D) 18.3 ππ
68. A particle is moving in a circular path of radius a under the action of an attractive potential π = βπ
2π2. Its
total energy is:
(A) π
2π2
(B) Zero
(C) β3
2
π
π2
(D) βπ
4π2
69. A parallel plate capacitor of capacitance 90 pF is connected to a battery of emf 20V. If a dielectric material
of dielectric constant πΎ =5
3 is inserted between the plates, the magnitude of the induced charge will be:
(A) 0.3 nC
(B) 2.4 nC
(C) 0.9 nC
(D) 1.2 nC
70. A silver atom in a solid oscillates in simple harmonic motion in some direction with a frequency of
1012 π ππβ . What is the force constant of the bonds connecting one atom with the other? (Mole wt. of silver =
108 and Avagadro number = 6.02 Γ 1023ππ ππππβ1)
(A) 7.1π πβ
(B) 2.2 π πβ
(C) 5.5 π πβ
(D) 6.4 π πβ
71. It is found that if a neutron suffers an elastic collinear with deuterium at rest, fractional loss of its energy is
ππ ; while for its similar collision with carbon nucleus at rest, fractional loss of energy is ππ. The values of ππ
and ππ are respectively.
(A) (.28, .89)
(B) (0 0)
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(C) (0, 1)
(D) (.89, .28)
72. The dipole moment of a circular loop carrying a current I, is m and the magnetic field at the centre of the
loop is π΅1. When the dipole moment is doubled by keeping the current constant, the magnetic field at the centre
of the loop is π΅2 . The ration π΅1
π΅2 is:
(A) β3
(B) β2
(C) 1
β2
(D) 2
73. In a potentiometer experiment, it is found that no current passes through the galvanometer when the
terminals of the cell are connected across 52 cm of the potentiometer wire. If the cell is shunted by a resistance
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of 5 Ξ©, balance is found when the cell is connected across 40 cm of the wire. Find the internal resistance of the
cell.
(A) 1.5Ξ©
(B) 2Ξ©
(C) 2.5Ξ©
(D) 1Ξ©
74. A telephonic communication service is working at carrier frequency of 10 GHz. Only 10% of it is utilized
for transmission. How many telephonic channels can be transmitted simultaneously if each channel requires a
bandwidth of 5 kHz?
(A) 2 Γ 104
(B) 2 Γ 105
(C) 2 Γ 106
(D) 2 Γ 103
75. Unpolarized light of intensity I passes through an ideal polarizer A. Another identical polarizer B is placed
behind A. The intensity of light beyond B is found to be 1
2. Now another identical polarizer C is placed between
A and B. The intensity beyond B is now found to be 1
8. The angle between polarizer A and C is
(A) 30π
(B) 45π
(C) 60π
(D) 0π
76. On interchanging the resistances, the balance point of a meter bridge shifts to the left by 10cm. The
resistance of their series combination is 1πΞ©. How much was the resistance on the left slot before
interchanging the resistances?
(A) 505 Ξ© (B) 550 Ξ© (C) 910 Ξ© (D) 990 Ξ©
77. From a uniform circular disc of radius R and mass 9 M, a small disc of radius π
3 is removed as shown in the
figure. The moment of inertia of the remaining disc about an axis perpendicular to the plane of the disc and
passing through centre of disc is:
(A) 40
9ππ 2
(B) 10ππ 2
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(C) 37
9ππ 2
(D) 4ππ 2
78. In a collinear collision, a particle with an initial speed π£0 strikes a stationary particle of the same mass. If
the final total kinetic energy is 50% greater than the original kinetic energy, the magnitude of the relative
velocity between the two particles, after collision, is:
(A) β 2 π£0
(B) π£0
2
(C) π£0
β2
(D) π£0
4
79. An EM wave from air enters a medium. The electric fields are οΏ½βοΏ½ 1= πΈ01π₯ cos [2ππ£ (π§
πβ π‘)] in air and οΏ½βοΏ½ 2 =
πΈ02οΏ½ΜοΏ½ cos[π(2π§ β ππ‘)] in medium, where the wave number k and frequency v refer to their values in air. The
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medium is non-magnetic. If ππ1 and ππ2 refer to relative permittivities of air and medium respectively, which of
the following, option is correct?
(A) ππ1
ππ2 = 2
(B) ππ1
ππ2 =
1
4
(C) ππ1
ππ2 =
1
2
(D) ππ1
ππ2 = 4
80. For an RLC circuit driven with voltage of amplitude π£π and frequency π0 =1
βπΏπΆ the current exhibits
resonance. The quality factor, Q is given by
(A) π0π
πΏ
(B) π
(π0πΆ)
(C) πΆπ
π0
(D) π0πΏ
π
81. All the graphs below are intended to represent the same motion. One of them does it incorrectly. Pick it up.
(A)
(B)
(C)
(D)
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82. Two batteries with e.m.f. 12 V and 13 V are connected in parallel across a load resistor of 10Ξ©. The internal
resistances of two batteries are 1Ξ© and 2Ξ© respectively. The voltage across the load lies between:
(A) 11.5 V and 11.6 V
(B) 11.4 and 11.5 V
(C) 11.7 V and 11.8 V
(D) 11.6 V and 11.7 V
83. A particle is moving with a uniform speed in a circular orbit of radius R in a central force inversely
proportional to the ππ‘β power of R. If the period of rotation of the particle is T, then:
(A) π β π π
2+1
(B) π β π π+1
2
(C) π β π π 2β
(D) π β π 3 2β for any n
84. If the series limits frequency of the Lyman series is π£πΏβ² then the series limits frequency of the P fund series
is:
(A) 16π£πΏ
(B) π£πΏ
16
(C) π£πΏ
25
(D) 25π£πΏ
85. In an a.c circuit, the instantaneous e.m.f. and current are given by
π = 100 sin 30π‘
π = 20 sin (30π‘ βπ
4)
In one cycle of a.c., the average power consumed by the circuit and the wattles current are, respectively:
(A) 1000
β2, 10
(B) 50
β2, 10
(C) 50,0
(D) 50,10
86. Two moles of an ideal monoatomic gas occupies a volume V at 27ππΆ. The gas expands adiabatically to a
volume 2V. Calculate (π) the final temperature of the gas and (π) change in its internal energy.
(A) (π) 195 πΎ (π) β 2.7 ππ½
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(B) (π) 189 πΎ (π) β 2.7 ππ½
(C) (π) 195 πΎ (π) 2.7 ππ½
(D) (π) 189 πΎ (π) 2.7 ππ½
87. A solid sphere of radius r made of a soft material of bulk modulus K is surrounded by a liquid in a
cylindrical container. A massless piston of area a floats on the surface of the liquid, covering entire cross
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section of cylindrical container. When a mass m is placed on the surface of the piston to compress the liquid,
the fractional decrement in the radius of the sphere, (ππ
π), is:
(A) πΎπ
3ππ
(B) ππ
3ππ΄
(C) ππ
πΎπ
(D) πΎπ
ππ
88. A granite rod of 60 cm length is clamped at its middle point and is set into longitudinal vibrations. The
density of granite is 2.7 Γ 103 ππ π3β and its Youngβs modulus is 9.27 Γ 1010 ππ. What will be the
fundamental frequency of the longitudinal vibrations?
(A) 2.5 kHz
(B) 10 kHz
(C) 7.5 kHz
(D) 5 kHz
89. The mass of a hydrogen molecule is 3.32 Γ 10β27ππ. If 1023 hydrogen molecules strike, per second, a
fixed wall of area 2 ππ2 at an angle of 45π to the normal, and rebound elastically with a speed of 103 π π β ,
then the pressure on the wall is nearly:
(A) 4.70 Γ 103 π π2β (B) 2.35 Γ 102 π π2β
(C) 4.70 Γ 102 π π2β (D) 2.35 Γ 103 π π2β
90. Seven identical circular planar disks, each of mass M and radius R are welded symmetrically as shown. The
moment of inertia of the arrangement about the axis normal to the plane and passing through the point P is:
(A) 55
2ππ 2
(B) 73
2ππ 2
(C) 181
2ππ 2
(D) 19
2 ππ 2